Zalmay Khalilzad's comments come as renewed fighting for days has plagued Afghanistan's southern Helmand province.
The Taliban pledge came after a meeting with U.S. peace envoy Zalmay Khalilzad and U.S. Gen. Austin Miller.
The announcement of U.S. strikes comes after a gun battle on Monday was reported in and around Lashkar Gah.
U.S. President Donald Trump has vowed to bring American troops home by Christmas.
Taliban spokesman Zabihullah Mujahed said Trump's statement was welcome and he considered it a positive step.
The Taliban are pushing for a return to power, having signed a landmark troop withdrawal deal with Washington.
The Taliban have continued attacks even as peace talks with the Kabul government are underway.
The airstrikes come as Taliban and government-appointed negotiators are meeting for the first time in Qatar.
The embassy didn't provide specifics, including how imminent the threat is.
The U.N. Security Council unanimously adopted a resolution welcoming the start of negotiations.
In a letter to VA Secretary Robert Wilkie, Rep. Elaine Luria, D-Va., said the plan was developed with no notice to Congress.
USAA Federal Savings Bank is part of USAA, which has about 13 million military and veteran-affiliated members.
The Army has said they are looking into the soldier’s actions for potential safety violations.
Two senators say the new Army Combat Fitness Test sets unrealistic standards for some soldiers.
The Marine Corps has officially retired the AH-1W Super Cobra helicopter.